On nonlinear parabolic equations with singular lower order term

2021 ◽  
Author(s):  
Youssef El hadfi ◽  
Mounim El ouardy ◽  
Aziz Ifzarne ◽  
Abdelaaziz Sbai
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Order Term ◽  
Nonlinear Parabolic Equations ◽  
Lower Order Term ◽  
Nonlinear Parabolic

scholarly journals Existence of a renormalized solution of nonlinear parabolic equations with lower order term and general measure data

2021 ◽  
Vol 39 (3) ◽  
pp. 93-114
Author(s):  
A. Marah ◽  
Abdelkader Bouajaja ◽  
H. Redwane
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Order Term ◽  
Nonlinear Parabolic Equations ◽  
Lower Order Term ◽  
Measure Data ◽  
General Measure ◽  
Renormalized Solution ◽  
Nonlinear Parabolic ◽  
The Right

We give an existence result of a renormalized solution for a classof nonlinear parabolic equations@b(u)/@t div(a(x; t;grad(u))+ H(x; t;ru) = ,where the right side is a general measure, b is a strictly increasing C1-function,div(a(x; t;grad(u)) is a Leray{Lions type operator with growth  in grad(u)and H(x; t;grad(u) is a nonlinear lower order term which satisfy the growth condition with respect to grad(u).

Existence results for a class of nonlinear parabolic equations with two lower order terms

2014 ◽  
Vol 41 (2) ◽  
pp. 207-219
Author(s):  
Ahmed Aberqi ◽  
Jaouad Bennouna ◽  
M. Hammoumi ◽  
Mounir Mekkour ◽  
Ahmed Youssfi
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Existence Results ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

scholarly journals A non-existence result for nonlinear parabolic equations with singular measures as data

2009 ◽  
Vol 139 (2) ◽  
pp. 381-392 ◽  
Author(s):  
Francesco Petitta
Keyword(s):  
Laplace Operator ◽  
Lower Order ◽  
Parabolic Equations ◽  
Existence Result ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Singular Measures ◽  
Nonlinear Parabolic ◽  
Image Position ◽  
Lower Order Terms

In this paper we prove a non-existence result for nonlinear parabolic problems with zero lower-order terms whose model iswhere Δp=div(|∇u|p−2∇u) is the usual p-laplace operator, λ is measure concentrated on a set of zero parabolic r-capacity (1<p<r) and q is large enough.

scholarly journals On the maximum principle for a class of nonlinear parabolicequations

2017 ◽  
Vol 21 (6) ◽  
pp. 89-92
Author(s):  
A.A. Kon’kov
Keyword(s):  
Maximum Principle ◽  
Nonlinear Equations ◽  
Wide Class ◽  
Lower Order ◽  
Parabolic Equations ◽  
Linear Equations ◽  
Nonlinear Parabolic Equations ◽  
Spatial Variables ◽  
The Maximum Principle ◽  
Nonlinear Parabolic

In this paper, we consider solutions of nonlinear parabolic equations in the half-space.It is well-known that, in the case of linear equations, one needs to impose additional conditions on solutions for the validity of the maximum principle. The most famous of them are the conditions of Tikhonov and T¨acklind. We show that such restrictions are not needed for a wide class of nonlinear equations. In so doing, the coefficients of lower-order derivatives can grow arbitrarily as the spatial variables tend to infinity.We give an example which demonstrates an application of the obtained re- sults for nonlinearities of the Emden - Fowler type.

scholarly journals Obstacle parabolic equations in non-reflexive Musielak-Orlicz spaces

2018 ◽  
Vol 4 (2) ◽  
pp. 189-206
Author(s):  
Ahmed Aberqi ◽  
Jaouad Bennouna ◽  
Mhamed Elmassoudi
Keyword(s):  
Parabolic Equation ◽  
Vector Field ◽  
Lower Order ◽  
Parabolic Equations ◽  
General Class ◽  
Order Term ◽  
Orlicz Spaces ◽  
Penalization Method ◽  
Nonlinear Parabolic ◽  
Monotone Vector Field

AbstractWe prove existence of entropy solutions to general class of unilateral nonlinear parabolic equation in inhomogeneous Musielak-Orlicz spaces avoiding ceorcivity restrictions on the second lower order term. Namely, we consider$$\left\{ \matrix{ \matrix{ {u \ge \psi } \hfill & {{\rm{in}}} \hfill & {{Q_T},} \hfill \cr } \hfill \cr {{\partial b(x,u)} \over {\partial t}} - div\left( {a\left( {x,t,u,\nabla u} \right)} \right) = f + div\left( {g\left( {x,t,u} \right)} \right) \in {L^1}\left( {{Q_T}} \right). \hfill \cr} \right.$$The growths of the monotone vector field a(x, t, u, ᐁu) and the non-coercive vector field g(x, t, u) are controlled by a generalized nonhomogeneous N- function M (see (3.3)-(3.6)). The approach does not require any particular type of growth of M (neither Δ2 nor ᐁ2). The proof is based on penalization method.

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